In this paper, we introduce a novel graph reduction technique, which we use as a preliminary step to count complete subgraphs in large networks. In [1]}, we generalised the concept of a rich-club [2]}, [3]}, [4]}, [5]}.
While the rich-club ranks vertices by their degree (i.e., the number of complete graphs of order 2 incident to the vertex), our generalisation of the rich-club ranks vertices by the number of complete graphs of order \(r\)  incident to the vertex.
